Respuesta :
[tex]\bf 3x+y=15\implies y=-3x+15\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-3\implies -\cfrac{3}{1}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{1}{3}}\qquad \stackrel{negative~reciprocal}{\cfrac{1}{3}}}[/tex]
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The slope of a line perpendicular to 3x + y =15 is 1/3. Thus, the correct option is C.
What is the equation of a line?
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
In the given equation 3x + y =15, the slope of the line will be,
3x + y = 15
y = 15 - 3x
y = -3x + 15
Thus, the slope of the equation is -3.
Now, the product of the slope of two perpendicular lines is always equal to -1. Therefore, the product can be written as,
-3 × m = -1
m = -1/-3
m = 1/3
Hence, the slope of a line perpendicular to 3x + y =15 is 1/3. Thus, the correct option is C.
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